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1999 | 133 | 2 | 175-186
Tytuł artykułu

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_0$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).
Słowa kluczowe
Czasopismo
Rocznik
Tom
133
Numer
2
Strony
175-186
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-05-11
poprawiono
1998-08-24
Twórcy
autor
  • Department of Mathematics, Agder College, Tordenskjoldsgate 65, N-4604 Kristiansand, Norway, Asvald.Lima@hia.no
autor
  • Faculty of Mathematics, Tartu University, Vanemuise 46, EE-2400 Tartu, Estonia, eveoja@math.ut.ee
Bibliografia
  • [1] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439.
  • [2] C.-M. Cho, The metric approximation property and intersection properties of balls, J. Korean Math. Soc. 31 (1994), 467-475.
  • [3] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
  • [4] M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 38-49.
  • [5] T. Figiel, Factorization of compact operators and applications to the approximation problem, Studia Math. 45 (1973), 191-210.
  • [6] G. Godefroy, N. J. Kalton and P. D. Saphar, Unconditional ideals in Banach spaces, ibid. 104 (1993), 13-59.
  • [7] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [8] P. Harmand, D. Werner and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993.
  • [9] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
  • [10] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345.
  • [11] Å. Lima, Uniqueness of Hahn-Banach extensions and liftings of linear dependences, Math. Scand. 53 (1983), 97-113.
  • [12] Å. Lima, The metric approximation property, norm-one projections and intersection properties of balls, Israel J. Math. 84 (1993), 451-475.
  • [13] Å. Lima, Property (wM*) and the unconditional metric compact approximation property, Studia Math. 113 (1995), 249-263.
  • [14] J. Lindenstrauss, On a problem of Nachbin concerning extension of operators, Israel J. Math. 1 (1963), 75-84.
  • [15] J. Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. 48 (1964).
  • [16] J. Lindenstrauss, On projections with norm 1-an example, Proc. Amer. Math. Soc. 15 (1964), 403-406.
  • [17] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977.
  • [18] E. Oja and M. Põldvere, On subspaces of Banach spaces where every functional has a unique norm-preserving extension, Studia Math. 117 (1996), 289-306.
  • [19] R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364, Springer, Berlin, 1993.
  • [20] W. M. Ruess and C. P. Stegall, Extreme points in duals of operator spaces, Math. Ann. 261 (1982), 535-546.
  • [21] I. Singer, Bases in Banach Spaces II, Springer, Berlin, 1981.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv133i2p175bwm
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